Experiments on a turbulent plume: shape analyses

Turbulent plume which is characterized by a large Reynolds number (Re >> 1) and buoyancy, is ubiquitous in nature, an example of which is a volcanic plume. As the turbulent plume rises, it entrains the ambient fluid and grows in size. There have been many laboratory experiments on turbulent plumes, but only few attempts were made to characterize the shape of the evolving plume as a function of source parameters (initial velocity and buoyancy). Here we report the results of laboratory experiments on a turbulent plume, a simplified model of a volcanic plume, to study how the shape of the plume changes as a function of time. Water and aqueous solutions of condensed milk, NaCl and CsCl, colored with a fluorescent dye are injected downward through an orifice (ID 1 mm) into a water contained in an acrylic tank with a cross-section of 30cm ¥times 30cm and a height of 50cm. Plumes with a density difference of 0.00 < ¥Delta ¥rho < 8.00 ¥times 10^ 2 (¥mbox{kg m}^ {-3}) and Re in the range and 210 < Re < 2850, are generated. These experimental parameters (initial Re, buoyancy) were chosen so that they cover the range from inertia-driven to buoyancy-driven regime. We find that the plume shape changes with time as instability and entrainment proceeds. In the beginning it is finger-like, but with time, plume head and vortices develop, and finally it transforms into a cone-like self-similar shape. After transforming a "cone-like" shape, sometimes a "head" appears again. We devise new methods to quantitatively characterize these changes of shape. Here we use (1) the height of the centroid of the plume shape and (2) the deviation from the self-similar triangular shape. Using these methods, we defined 4 regimes as a function of time. We find that the onset times of the 4 regimes have a negative power-law relations on initial Re, which scale better than using onset heights. Importantly, we find that the buoyancy causes the regime transitions to become earlier. Our experiments suggest that monitoring the change of the shape of the rising volcanic plumes and analyzing the regime transition times can be used to constrain the effective initial Re and buoyancy of the plumes.